The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by...The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if (A, C, ψ) is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and (α, β )-Yetter-Drinfeld modules as examples.展开更多
Let (C, C) be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category (C, C) is investigated. First, a braided C2-commutative algebra i...Let (C, C) be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category (C, C) is investigated. First, a braided C2-commutative algebra in the category (C, C) is defined and three equations on the braiding in the category (C, C) are proved. Secondly, it is verified that (A, [, ] ) is a left (strict) Jacobi braided Lie algebra if and only if (A, [, ] ) is a braided Lie algebra, where A is an associative algebra in the category (C, C). Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel'd modules and the category of Hopf bimodules.展开更多
Here, we report our experience with a case of severe biliary bleeding due to a hepatic arterial pseudoaneurysm that had developed 1 year after endoscopic biliary plastic stent insertion. The patient, a 78-year-old wom...Here, we report our experience with a case of severe biliary bleeding due to a hepatic arterial pseudoaneurysm that had developed 1 year after endoscopic biliary plastic stent insertion. The patient, a 78-year-old woman, presented with hematemesis and obstructive jaundice. Ruptured hepatic arterial pseudoaneurysm was diagnosed, which was suspected to have been caused by long-term placement of an endoscopic retrograde biliary drainage(ERBD) stent. This episode of biliary bleeding was successfully treated by transarterial embolization(TAE). Pseudoaneurysm leading to hemobilia is a rare but potentially fatal complication in patients with long-term placement of ERBD. TAE is a minimally invasive procedure that offers effective treatment for biliary bleeding.展开更多
We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of...We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.展开更多
Let A and H be Hopf algebra, T-smash product AT H generalizes twisted smash product A * H. This paper shows a necessary and sufficient condition for T-smash product moduie category AT HM to be braided monoidal category.
Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoi...Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoidal category HHYDQCM is introduced and the specific structure maps are given.Thirdly,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is discussed.It proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.展开更多
The faithful quasi-dual H^d and strict quasi-dual H^d' of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H^d' is an H-Hopf module. A connection between the integrals ...The faithful quasi-dual H^d and strict quasi-dual H^d' of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H^d' is an H-Hopf module. A connection between the integrals and the maximal rational H^d-submodule Hdrat of Hd is found. That is, H^drat ≌∫Hdl ×H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld category (BBYD, C) are given.展开更多
In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of w...In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalencebetween the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in abraided monoidal category and the category of Hopf algebras in the non-strict braided monoidal category ofleft-left Yetter-Drinfeld modules over H.展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20060286006)the National Natural Science Founda-tion of China(No.10571026)
文摘The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if (A, C, ψ) is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and (α, β )-Yetter-Drinfeld modules as examples.
基金The National Natural Science Foundation of China(No.10871042)
文摘Let (C, C) be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category (C, C) is investigated. First, a braided C2-commutative algebra in the category (C, C) is defined and three equations on the braiding in the category (C, C) are proved. Secondly, it is verified that (A, [, ] ) is a left (strict) Jacobi braided Lie algebra if and only if (A, [, ] ) is a braided Lie algebra, where A is an associative algebra in the category (C, C). Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel'd modules and the category of Hopf bimodules.
基金Supported by Japanese Red Cross Kyoto Daiichi Hospital,Kyoto,Japan
文摘Here, we report our experience with a case of severe biliary bleeding due to a hepatic arterial pseudoaneurysm that had developed 1 year after endoscopic biliary plastic stent insertion. The patient, a 78-year-old woman, presented with hematemesis and obstructive jaundice. Ruptured hepatic arterial pseudoaneurysm was diagnosed, which was suspected to have been caused by long-term placement of an endoscopic retrograde biliary drainage(ERBD) stent. This episode of biliary bleeding was successfully treated by transarterial embolization(TAE). Pseudoaneurysm leading to hemobilia is a rare but potentially fatal complication in patients with long-term placement of ERBD. TAE is a minimally invasive procedure that offers effective treatment for biliary bleeding.
基金Supported by National Natural Science Foundation of China under Grants No.10875026
文摘We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.
文摘Let A and H be Hopf algebra, T-smash product AT H generalizes twisted smash product A * H. This paper shows a necessary and sufficient condition for T-smash product moduie category AT HM to be braided monoidal category.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)。
文摘Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoidal category HHYDQCM is introduced and the specific structure maps are given.Thirdly,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is discussed.It proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.
文摘The faithful quasi-dual H^d and strict quasi-dual H^d' of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H^d' is an H-Hopf module. A connection between the integrals and the maximal rational H^d-submodule Hdrat of Hd is found. That is, H^drat ≌∫Hdl ×H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld category (BBYD, C) are given.
基金supported by Ministerio de Ciencia e Innovación,project MTM2010-15634 and by FEDER
文摘In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalencebetween the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in abraided monoidal category and the category of Hopf algebras in the non-strict braided monoidal category ofleft-left Yetter-Drinfeld modules over H.